The State of Texas may allow firearm possession by a felon after a certain amount of time but the federal government does not and federal law would override Texas law in this case.

18 USC 922(g):

Quote:

It shall be unlawful for any person—
(1)who has been convicted in any court of, a crime punishable by imprisonment for a term exceeding one year;
to ship or transport in interstate or foreign commerce, or possess in or affecting commerce, any firearm or ammunition; or to receive any firearm or ammunition which has been shipped or transported in interstate or foreign commerce.

It would also be a federal crime to knowingly provide a felon with a firearm.